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In the diagram, BD = 9, CE = 7, [ABC] = 30, and [ADE] = 20. Find [ACD]

 

https://latex.artofproblemsolving.com/4/4/a/44a0385ed03d62054a89d5f89dbfe8d93195d0b5.png

 Dec 11, 2019
 #1
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All triangles share the altitude.

 

Let CD be X. Let the shared altitude be Y.

 

Make some equations!

(1/2) * y(9-x) = 30

(1/2) * y(7-x) = 20

 

I think from here you pretty much solve for X and Y.

 

Once you have those values, you can do (1/2) * X * Y for the answer.

 

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 Dec 11, 2019
 #2
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Then we get [ACD] = 24.

 Dec 11, 2019

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